1. Field of the Invention
The present invention relates generally to a driveline and suspension system for a vehicle and, more particularly, relates to driveline-suspension coupling in a narrow multi-track leaning vehicle with three or more wheels and with at least two driving wheels.
2. Description of the Prior Art
Any discussion of the prior art throughout this disclosure should not be considered as an admission that such prior art is widely known or forms part of general knowledge in the field.
Need for a Narrow Vehicle
There is a perceived need to provide narrow vehicles, such as shown in FIG. 1, to travel in crowded environments, for example in or around cities for commuting on congested streets and expressways where traffic. Such a vehicle would be able to thread through informal gaps in traffic, split lanes when legal, and may be legal for use in high-occupancy vehicle commuting lanes. In addition to being able to thread through congested traffic, a narrow vehicle would be easier to park and store compared to a typical automobile. Special narrow-width commuter vehicle lanes which could be one-half lane width (or less) could be used to improve traffic flow within the same roadway width; a four lane expressway could be turned into an eight lane expressway by just adding additional lane lines. Narrowness also improves vehicle fuel efficiency because the vehicle frontal area would be approximately one-half that of a typical automobile. The vehicle will be lighter and require less material to build. This light weight also leads to improved fuel efficiency and improved performance.
Roll Instability Problems with Narrow Vehicles
This narrowness creates a problem with vehicle roll instability. The National Highway Traffic Safety Administration (NHTSA) uses the Static Stability Factor (SSF=Tk/(2*Hcg)), which is equal to the vehicle track width (Tk) divided by two times the vehicle Center of Gravity Height (Hcg), as a measure of vehicle roll stability. A vehicle with a lower SSF has a higher chance of rolling over. A typical automobile has a SSF between 1.3 to 1.5, while a typical SUV or pick-up truck has an SSF between 1.0 and about 1.3. A narrow vehicle may have a SSF as low as 0.20. This low level of roll stability limits the narrow vehicle to very mild maneuvers and low levels of lateral acceleration to prevent the vehicle from falling over. For reference, a motorcycle has an SSF of zero; and typical running mammals are below 0.2, which implies that these animals use some sort of active control of foot location, and are essentially “leaning vehicles.”
Ballast as a Solution
One solution to the problem of roll instability of narrow vehicles is to ballast the vehicle to reduce the center of gravity height (such as seen in U.S. Pat. No. 6,328,121). For any significant improvement in roll stability for a narrow width vehicle, large ballast weights would be required. Large, heavy ballast would negate many of the advantages of a narrow vehicle.
Vehicle Leaning as a Solution
Another solution is to cause the vehicle to lean into a corner, similarly to a motorcycle or running mammal. With enough leaning or tilting, the moment applied about the center of gravity (CG) by the lateral tire forces acting at ground level are reduced by the moment applied by the vertical tire forces holding the vehicle up, relative to the CG offset created by leaning the vehicle. For these moments to balance, such as on a motorcycle with narrow tires, the tangent of the lean angle from vertical (phi) is approximately equal to the Lateral Acceleration (L.A.≈tangent {Phi}). (Angle phi is in relation to true vertical.) These values are only approximately equal due to the tire width effecting the lateral location of the tire contact point due to lean; for an idealized motorcycle with zero width tires, the tangent of the lean angle from vertical is equal to the lateral acceleration for steady state cornering.
Leaning Vehicle Control Methods
There are two basic ways to control the lean of a narrow vehicle: free leaning and controlled leaning. In a free leaning narrow vehicle, the vehicle is designed to have a suspension roll stiffness which can be either close to zero (resulting in a “free leaning mode”), or stiff (resulting in a “locked roll mode”). For high speed or high lateral acceleration operation, the free leaning mode is selected, and the narrow vehicle acts like a standard motorcycle or single track vehicle. This is similar to a motorcyclist riding with his feet on the footrests. For slow speed, low lateral acceleration operation, the locked roll mode is selected, and the narrow vehicle acts as a standard multi-track vehicle with the suspension maintaining the vehicle upright. This is similar to a motorcyclist riding or stopping with his feet touching the ground.
As with a motorcycle, in the free leaning mode the operator must steer the vehicle for balance by controlling the tire contact patch location relative to the vehicle CG, thereby to apply roll moments from gravity acting on the vehicle CG. This switching between roll modes can be accomplished either by the operator alone, or with an automatic control system which determines, based on an algorithm, when to switch between the two roll stiffness modes. There may also be a hybrid system combining operator and automatic control. In a controlled leaning vehicle (e.g., as seen in U.S. Pat. Nos. 5,765,846 and 4,423,795), some form of automatic control and actuator system are used to control the suspension to lean the vehicle into a turn, or to use steering torques to control tire contact patch location, or a combination of the techniques.
A New Vehicle Type, Such as a Narrow Leaning Vehicle, Must have Better Stability and Dynamics than the Current Fleet
For a new type of narrow, multi-track vehicle to be viable, it must have at least the same and preferably better stability and dynamics than vehicles it would be supplementing or replacing in the current fleet. A “free leaning” narrow vehicle would be considered to be supplementing the motorcycle fleet because it would have similar dynamics to motorcycles. A “controlled leaning” narrow vehicle would be considered to be supplementing the automobile fleet, because the controlled leaning system would give the vehicle automobile-like dynamics not requiring “counter steer” by the driver. The new type vehicle must not have any “bad habits” or other instabilities as compared to the fleet it would be joining.
Required Lean Angles
For a narrow vehicle to perform adequately while sharing roadways with motorcycles, automobiles and heavier vehicles, relatively large lean angles equal or greater than 30° are required (Tan(30°)≈0.6 g lateral acceleration). To allow for 1 g lateral acceleration, a lean angle of approximately 45° is required. This amount of lean or tilt requires suspension wheel travels (up-and-down in the vehicle coordinate frame) on the order of the vehicle track width. For example, a vehicle with a 20-inch track width would require each wheel to have greater than ±10 inches of wheel travel from nominal ride height, assuming vertical suspension travel in the vehicle coordinate frame. It is difficult to achieve such a large amount of wheel travel, relative to track width, with conventional automotive suspension types on a driven axle (such as Short-Long-Arm (SLA), McPherson Strut, or Swing Axle suspensions) due mainly to the limits of drive shaft joint angularity on driven axles. Some prior art narrow leaning vehicles with multi-track driven wheels have used some form of trailing arm suspension, which can be more readily designed with the required amount of wheel travel for a given track width.
Known Narrow Leaning Vehicles with Trailing Arm Suspensions
Prior art narrow leaning vehicles with driven multi-track axles generally use chain or belt drive systems due to the large wheel travel required for adequate lean angles. To eliminate chain path variations as the driven wheel moves over the range of suspension travel, the driving pinion typically is located coaxially with the trailing arm pivot, such as the configuration shown in U.S. Pat. No. 4,003,443 to Boughers, a drawing figure from which is depicted in FIG. 2A herein. Some form of “static” chain path length adjustment is required in such configurations to adjust for wear and manufacturing tolerances. Other prior art leaning vehicles use a shaft drive to transmit the power to the trailing arm suspended wheels, in a similar fashion to shaft drive motorcycles; a shaft drive universal, or constant velocity, joint coaxially ordinarily is located to the trailing arm pivot axis.
Driveline-Suspension Coupling
Trailing arm suspensions exhibit a phenomenon called “driveline-suspension coupling” (DSC), in which longitudinal (i.e. front-to-back-to-front) driveline forces couple into vertical suspension forces and motions between the vehicle's sprung mass and unsprung mass. For a vehicle with rear drive, the DSC is termed “anti-squat” when it tends to extend the suspension during forward vehicle acceleration. While this is an inherent phenomenon in trailing arm suspensions, other types of suspension systems, such as short-long arm (sometimes also referred as double A-arm), semi-trailing arm, swing axle, McPherson or Chapman strut and multi-link independent suspension can be designed to have anti-squat behavior. “Driveline” refers generally to the powertrain assembly which finally delivers rotary power to the driven wheel(s) of a vehicle, including by example a looped chain or belt with operably connected driving and driven sprockets/pinions, also including a driveshaft and associated universal joints and links.
For a Multi-Track Leaning Vehicle DSC Creates Undesirable Roll Dynamics
This coupling between drive forces and suspension forces creates a roll stability problem in narrow multi-track leaning vehicles. For typical known geometries, such as shown in FIG. 2B-I, a large roll moment is created by the DSC which causes the vehicle to increase the lean of the vehicle as the drive forces are increased. In typical operation, this problem is expressed when the vehicle is exiting a turn and accelerating. As illustrated by FIG. 2B-I, the respective lifting forces LF, LF′ (acting on lines through the respective tire contact patch centroids, TrCpt and TrCpt′) are unequal during acceleration due to the anti-squat. Under this condition, the application of drive force causes the vehicle to lean into the turn even more, exactly the opposite of the operator's desires. This problem also creates an unstable and dangerous operating condition, since the drive forces increase vehicle speed while also tightening the turning radius, which requires increasing levels of tire traction. This is the first problem with known multi-track leaning vehicle driveline suspension geometries: unstable vehicle behavior during acceleration. Reference is made to FIG. 2B-II herein, showing a typical motorcycle during a turn. If it is assumed that the tires have zero width, then the lifting force LF created by driveline-suspension coupling lifts the motorcycle in the vehicle vertical plane only, and does not impart a deleterious roll moment. If tire width is considered, the tire contact patch centroid and the contact force shift to the left for a left turn, as indicated by the dotted line in FIG. 2B-II. This shifted force provides a slight restoring moment to the motorcycle, straightening it up as it is accelerated out of a turn.
Undesirable Roll Dynamics Only Affect Narrow Multi Track Vehicles
Narrow multi-track vehicles exhibit the foregoing undesirable roll dynamics which can cause vehicle instabilities and increased difficulty of operator control during combined operation of turning and longitudinal acceleration. Neither motorcycles (single track vehicles), nor automobiles (multi-track vehicles with small lean angles) exhibit these undesirable behaviors. For motorcycles, the tire forces acting in the vertical vehicle plane are reasonably aligned with the vehicle's center of gravity, and cannot produce a large roll moment acting on the vehicle. Although automobiles have a large track width between the right and left tires, the small lean angles and small suspension wheel travels associated with typical maneuvers do not provide very large differences between the respective anti-squat vertical lifting forces of the right and left suspensions. The roll moments created by these differences are small when compared to the roll moment created by the lateral acceleration during cornering and the roll stiffness provided by the suspension system. Thus, significant roll instability due to driveline-suspension coupling is unique to narrow multi-track vehicles, especially to such vehicles with free leaning control.
Suspension Coupling During Acceleration
Attention is now invited to FIG. 3, which presents four curves plotting applied roll moment (lb-ft) as a function of lean angle (degrees). The curves of the figure were plotted using the MATLAB program with empirical input. The curve A shows the magnitude of this destabilizing roll moment for a nominal narrow leaning vehicle with typical motorcycle chain-driven, rear trailing arm, geometry. It is assumed in FIG. 3 that both driven wheels have the same chain (or drive belt) tension and approximate driving force. (This equality could be realized with the use of a differential incorporated into the intermediate shaft, supplying power to both driver pinions of the final flexible loop drives to each of the driven wheels (see, e.g., U.S. Pat. No. 4,003,443). Some known narrow leaning vehicles have reduced the destabilizing drive-induced roll moment by increasing the trailing arm length, or by locating the driving pinion coaxially with the trailing arm pivot, or in some cases using driving pinion diameters equal to the driven pinion diameters (see, e.g., European Patent Publication EP1702773A2, website www.naro.co.uk, and U.S. Pat. No. 5,611,555, www.moebius.es/ccalleja/). FIG. 3 illustrates at curve B typical magnitudes of the unstable roll moment for a nominal narrow leaning vehicle incorporating such known drive geometries. Although such modifications reduce the destabilizing leaning moment, compared to that of the typical motorcycle drive geometry, the destabilizing roll moment is still relatively large. Increasing trailing arm length reduces the roll instability, but practical considerations impose a limit on the length of the trailing arm. This is the second problem with prior art narrow leaning vehicles: long trailing arms are difficult to contain within the vehicle envelope. In FIG. 3, curve C represents the roll moment during acceleration for an apparatus having an improved geometry according to the present disclosure, plotted with empirical data from a tested prototype, optimized for minimum roll moment. The geometry provides the least amount of roll disturbance from the driveline, which is stabilizing for lean angles below 40°. For larger lean angles, the roll moment is very slightly unstablizing (positive). Curve D of FIG. 3 depicts the roll moment during acceleration for a vehicle with the improved geometry, optimized for a minimum stabilizing geometry. This geometry always provides for a stabilizing geometry over the complete range of lean angles, although a slightly more stabilizing roll moment occurs over mid-range lean angles as compared to curve C.
To provide a better understanding of the magnitude of these DSCC-induced roll moments, FIG. 4A presents the roll moment of the nominal narrow leaning vehicle as a function of vehicle lean angle (Roll Moment=Vehicle Weight*Center of Gravity Height*Sine {Lean Angle}), assuming zero width tire contacts. FIG. 4B presents the data from FIG. 3, but normalized by the roll moment (due to vehicle lean) from FIG. 4A. (The Normalized Roll Moment due to forward thrust equals roll moment due to forward thrust divided by roll moment due to lean, all at a given lean angle). As combined reference to these graphs shows, the roll moments created from suspension coupling of drive force into suspension lift, can have a significant and unstable effect upon the turning dynamics of a narrow leaning commuter vehicle.
Suspension Coupling During Braking
In addition to the driving force creating an unstable vehicle condition, braking forces similarly can also create undesirable dynamic behavior. With the service brakes mounted onto the vehicle's trailing arm, which is typical for many motorcycles, a braking force (and resulting braking moment) acting on the trailing arm couple into the vertical suspension forces. The resulting applied roll moment, for a vehicle known in the art, is shown as curve A in FIG. 5A. In typical operation in which a rider is braking during turn initiation or during turning, this coupling between brake force and suspension forces tends to rotate the vehicle back toward true vertical, against the rider's desire to lean into the turn. Although this effect of this braking driveline-suspension coupling is not as potentially dangerous as the driving force coupling problem, the vehicle is more difficult to control than a typical motorcycle. This dynamic affect of a floating brake geometry, for a known vehicle, with the brake stay parallel to and of about equal length of the trailing arm, is indicated as curve B in FIG. 5A.
Curve C of FIG. 5A presents the roll moment during braking for a tested prototype apparatus according to this disclosure, with the improved geometry optimized for minimum roll moment over the range of suspension travel/lean angles. The innovative geometry provides the least amount of roll disturbance attributable to braking. For larger lean angles, the roll moment is very slightly “pro-lean in.” In the figure, curve D presents the roll moment during braking which had a lower roll moment due to braking in the mid-range of lean angles, but is more “pro-lean in” at the high lean angles. Compared to vehicles known in the art, either of these innovative geometries has negligible brake/roll coupling.
Reference is made to FIG. 5B, presenting enlarged detail of curves C and D from FIG. 5A, while FIGS. 5C and 5D present the normalized roll moment due to braking. This geometry improves the vehicle dynamics only slightly as compared to the typical geometry. This is the third problem with known narrow leaning vehicles: undesirably poor vehicle roll dynamics during braking. A fourth problem with known narrow leaning vehicles is that there is necessarily reduced vehicle performance, because power and braking performance are deliberately reduced in an effort to ameliorate vehicle stability and/or handling problems. A fifth problem with known narrow leaning vehicles is the increased vehicle operator training and/or skill levels required for operation, due to poor vehicle dynamic behavior and handling qualities.
Suspension Coupling During Engine Braking
Engine braking (as distinguished from service braking) in narrow leaning vehicles creates similar issues of coupling longitudinal forces into vertical suspension forces to create similar roll stability problems. This effect will be of comparatively smaller magnitude than for either engine drive or service braking, because engine braking torques are typically of smaller magnitude than engine drive or service braking torques.
The Dynamics of Trailing Arm Suspension
Confusion appears in the prior art about the dynamics of trailing arm suspensions. Trailing arm suspensions have been used in multi-track vehicles as well as in single track vehicles. An excellent reference for multi-track vehicle suspensions is Milliken, although little is discussed therein concerning “pure trailing arm” suspensions. Milliken, W. F., et al., “Race Car Vehicle Dynamics,” SAE International, Warrendale, Pa., 1995. (ISBN 1-56091). This may be because modern multi-track vehicles do not, in general, use this type of suspension. Milliken notes that the pure trailing arm suspension type has structural and weight problems. (The wheel essentially is cantilevered from the trailing arm pivot, and the trailing arm therefore must be strong in bending in all directions.) The pure trailing arm also has performance issues (no camber gain of the wheel, no toe change and the roll center is on the ground). The Milliken authors review only a basic trailing arm type, with the wheel brake fixed to the trailing arm and the wheel driven by a half-shaft, parallel to the trailing arm pivot axis, from a sprung mass-mounted differential. The variations of trailing arm suspensions, such as floating brakes, shaft, or chain drive are not discussed. Nor are the effects of large vehicle roll angles. This may be expected, as most multi-track vehicles generally limit roll angles to less than ±10°.
In contrast to most multi-track vehicles, modern single track vehicles (motorcycles) universally use trailing arm suspensions on the rear, although it typically is called a “swing arm” suspension. This is unsurprising, as the problems associated with employing trailing arm suspensions in multi-track vehicles become advantages in single track vehicles (where to cantilever the suspension from the center of the vehicle and to have no camber gain, no toe change, and a roll center located on the ground are desirable). Because the trailing arm suspension is the dominate rear suspension type for single-track vehicles, considerable effort has been spent on developing it and its variations for motorcycles as well as bicycles. There are three basic known variations, which will be called: simple trailing arm (similar to Milliken “pure trailing arm”), trailing arm with torque link, and arbitrary trailing arm with torque link. To reduce the confusion on trailing arm suspension dynamics, and to place the present invention in context with these dynamics, a brief review will be presented.
Load Transfer Due to Acceleration
When a ground vehicle is accelerated, the tires produce forces acting on the ground to accelerate the vehicle. Because the vehicle's center of gravity is above the ground, the tire forces create a moment which pitches or rolls the vehicle forward (or backward), and which changes the vertical load on the tires. This change in load is called load transfer. If the vehicle has suspension, this load transfer creates suspension motions: forward acceleration generates front lift and rear squat, while deceleration creates front dive and rear rise. In addition to acceleration creating these load transfers, aerodynamic forces and slopes will also produce load transfer, but this will not be discussed further. The vehicle parameters which affect longitudinal load transfer are the vehicle wheelbase, center of gravity height, mass, and the actual acceleration. The longitudinal position of the mass does not affect the load transfer, but does affect the actual loads on the tires. If a vehicle can accelerate sufficiently quickly, the load transfer can reduce the respective tire load to zero lifting the tire off the ground (a “wheelie” or a “stoppie”), creating a pitch instability.
Thus, as a vehicle accelerates forward or decelerates (during braking), a load transfer occurs between the front and rear of the vehicle, attributable in part to the above-ground height of the vehicle's center of gravity, which creates a moment during the longitudinal acceleration. The load transfer ordinarily compresses and extends the suspension. With suspension coupling, as provided by a driveline suspension coupling coefficient, some of this load transfer is reacted by the suspension linkages. In the case of a motorcycle or a suspension according to the present disclosure, this linkage reaction is through the trailing arm suspension and drive element (i.e., chain or shaft drive) and in the case of braking, though a brake torque link or the like. In the case of 0% anti-squat, the linkages provide no reaction to the acceleration moment (due to the center of gravity above the ground). In the case of 100% anti-squat, the linkage provides sufficient reaction to counterbalance exactly the load transfer due to the acceleration moment. With more than 100% anti-squat, the rear of the vehicle actually will lift up during acceleration, rather than squatting (a somewhat unnerving behavior of some shaft-drive motorcycles). The force split between the linkages and the springs does not change the load transfer on the tires which is only a function of the acceleration and the height of the center of gravity.
The load transfer during acceleration has important effects on vehicle behavior. The load transfer from the suspension springs reacts to motion of the sprung mass, so when a vehicle is accelerated, the following effects occur: 1) the tires push forward the bottom of the sprung mass; 2) the sprung mass rotates; 3) such rotation compresses/extends the suspension springs (and tires also); and 4) the springs push on the tires more or less. As a result, the load transfer due to acceleration is applied to the tire ground contact patches. This process takes time and the springs cushion the sprung mass and smooth out the load transfer.
The load transfer from the suspension linkage reacts to the forces applied to the linkage. This creates a direct path from the longitudinal forces provided by the tires into the sprung mass, there is no cushioning or time delay due to motion of the sprung mass. Also, the load transfer through the suspension linkages typically puts more force into the linkages. This can add to the “stiction” (static friction) to the suspension which tends to “lock up” the suspension reducing the suspension suppleness and vehicle ride quality. Motorcycles frequently are provided with roller bearings in the trailing arm pivots, with the result that static friction is less of an issue.
DSC Anti-Squat and Anti-Rise in Rear Suspensions
Anti-squat, as a result of driveline-suspension coupling (DSC), in a rear suspension reduces the motion of the suspension due to load transfer. As mentioned above, trailing arm suspensions naturally exhibit this behavior due to DSC, which is a function of the drivetrain and suspension geometry (kinematics), and not the suspension's force components (suspension kinetics, i.e., springs or dampers). During forward acceleration, due to DSC the suspension linkages (primarily the trailing arm and/or torque link) tend to push the unsprung mass (including e.g., trailing arm and wheel) down toward the ground and to lift the sprung mass (reducing the rear squat due to load transfer). Conversely, during forward deceleration, the suspension linkages tend to lift the unsprung mass and to pull downward the sprung mass (which has a relatively reduced effect because the tire on the driven wheel can be lifted off the ground, thereby reducing tire traction).
Quantifying Anti-Squat and Anti-Rise in Simple Trailing Arm Rear Suspensions
Reference to FIG. 6 conveys understanding of DSC effects during the acceleration of a vehicle having a trailing arm suspension. FIG. 6 illustrates a simple prior art trailing arm rear suspension on a motorcycle 50. The complete system includes a trailing arm 51, a rear wheel 54 (rotatable around wheel axis Wp), a motorcycle sprung mass 63, a front suspension 64 and a front wheel 65. A driving torque DT is applied between the trailing arm 51 and the wheel 54, which torque generates a driving force DF acting at the ground on a tire contact patch (at TrCpt in the figure) pushing the vehicle 50 forward. A reaction torque RT, which is equal and opposite to the DT, is applied to the trailing arm 51 (assuming the trailing arm has no mass or inertia). The RT acts tending to rotate the trailing arm 51 backwards (per direction arrow RT in the figure), lifting the motorcycle's sprung mass 63 via the trailing arm pivot TAp, and extending the suspension. The driving force DF ultimately acts through the trailing arm pivot TAp with both a horizontal force HF and vertical force LF, as seen FIG. 6. These forces are components of a single resultant force R acting along an imaginary line defined between the tire contact patch centroid TrCpt and the trailing arm pivot TAp. This imaginary line is called the “Line of Action,” LoA. The lifting force LF acts against the squat (that is, squat due to due to load transfer), and reacts through the TrCpt in a plane perpendicular to the trailing arm pivot axis TAp. This lifting force is analogous to the destabilizing lifting forces shown diagrammatically in FIG. 2B-I. In the case of a braking torque, the forces have negative values (reversed in direction), but have the same geometry. The trailing arm pivot (TAp) is an important point (in the two-dimensional vehicle vertical plane), because the forces acting between the unsprung mass (primarily the trailing arm 51 and wheel 54) and the sprung mass 63, occur at this point. Because of this importance, the trailing arm pivot is given an addition name, the “Actual pivot and Force center” labeled ApFc in the figures.
FIG. 7 is a top sectional view of a prior art shaft drive, simple trailing arm, motorcycle rear suspension (similar to that seen in FIG. 6) cut along a plane defined by the trailing arm pivot TAp and the wheel axis Wp. Rotary power is transmitted via a drive shaft 62. The driving torque DT is created by a driving pinion 57 working against a crown wheel 58. A braking torque can be created by the brake caliper 59 working against the brake disc 60. A torque on the drive shaft 62 or a universal joint 61 is reacted by the trailing arm pivot axis TAp, and does not impart torque to swing the arm 51 about the pivot axis TAp. If provided, a hub motor could provide torque in a similar manner as the shaft drive, producing torque between the trailing arm 51 and the wheel 54.
FIG. 8 provides a side view of the motorcycle 50 of FIG. 6 without the rear wheel 54 and trailing arm 51 shown. Shown in FIG. 8 are two possible pivot locations on the sprung mass, first trailing arm pivot TAp1 and second trailing arm pivot TAp2, with corresponding lines of action, first line of action LoA1 and second line of action LoA2. LoA1 is drawn from the tire contact patch centroid through the location of the center of gravity CG for the vehicle system, while LoA2 is drawn from the centroid of the tire contact patch through the point of intersection of a vertical line through the front axle and the horizontal line at the center of gravity height, Hcg. These lines and pivot locations are impractical, but they illustrate two important special cases.
To simplify the analysis, it is assumed that the CG is located evenly between the two wheels of the motorcycle (e.g., at about one-half the wheelbase length), and that the Hcg is equal to one-half the wheelbase. It also is assumed that the suspension forces act vertically in line with the locations of the respective front and rear wheel axes. (It should be noted that although these assumptions are made, if the front suspension were at the true fork angle, that the rear suspension were not located in line with the rear axle, and the CG was closer to either end, identical results could be determined but the real issues would be obscured by needless detail.) In addition to the above innocuous assumptions, it is assumed that the unsprung masses at each end of the vehicle are mass-less, and that full rear tire driving force DF is used to accelerate the sprung mass only.
For the first case with LoA1 passing through the CG, during acceleration the lifting force LF1 equals the driving force DF1. If the vehicle accelerates at 1 g, then the LF1 equals the total vehicle weight, and the suspension force that was holding up the rear up lifts the sprung mass until the suspension spring (not shown) is unloaded. Not only does the vehicle's rear not “squat,” it lifts up significantly and prevents the sprung mass from pitching because the front suspension is not loaded by the acceleration.
Continued reference is made to FIG. 8. For the second case with LoA2 passing through the Hcg above the front axle, the lifting force LF2 equals half the driving force DF2. If the vehicle accelerates at 1 g, then LF2 just counteracts the increase in load transfer due to acceleration. The rear suspension neither lifts nor squats, although the front suspension lifts due to load transfer away from the front. This condition and geometry is considered to be 100% anti-squat. (If the unsprung masses weren't zero, than some of the driving force DF would be required to accelerate the rear unsprung mass and the lifting force LF would be slightly smaller, so the anti-squat would be slightly less than 100%). A third fanciful case may also be considered in which the trailing arm pivot TAp is located on the ground and the LoA also is directed on the ground. Although impractical, the LF would be zero and there would be 0% anti-squat.
FIG. 9 illustratively summarizes the foregoing discussion, and depicts different lines of action (from the rear tire contact patch centroid) for a given percent anti-squat. Case 2 is represented in FIG. 9 by the 100% anti-squat line of action (directed between the tire contact patch and the intersection of the line at center of gravity height Hcg, as also depicted in FIG. 8). (A case number 1 isn't shown in FIG. 9, but would represent 200% anti-squat.) A 50% anti-squat line is halfway (along the vertical line through the front wheel axis) between the 100% and 0% anti-squat lines, with the 0% anti-squat LoA being at ground level. A minus fifty percent (−50%) anti-squat line of action is shown, representing a pro-squat case, in which the lifting force LF is negative and increases the vehicle squat by pulling the rear of the vehicle down during forward acceleration.
The above figures imply that avoiding an excessively high anti-squat DSC effect is fairly difficult with typical shaft drive motorcycle geometries. These high amounts of anti-squat create an undesirable up and down motion of the motorcycle as the throttle is changed. For motorcycles with high power levels, the rear suspension may extend to full droop under acceleration, effectively locking up the rear suspension. The suddenly changing tire loads due to throttle application can also excite tire hopping and chatter, which reduces traction for both longitudinal and lateral directions.
Anti-Squat in Trailing Arm with Torque Link Rear Suspensions
FIG. 10 presents a side view of a prior art (Moto Guzzi® V11 Sport) trailing arm with torque link rear suspension on the motorcycle 70. The system includes a trailing arm 71, a torque link 72, a crown wheel carrier 76, an axle 75 (with axis Wp), a rear wheel 74, a motorcycle sprung mass 83, a front suspension 64 and a front wheel 65. The trailing arm 71 is revolutely mounted to the sprung mass 83 by the trailing arm pivot TAp. The rear wheel axle 75 is fixed to the trailing arm 71 parallel to the trailing arm pivot TAp. The crown wheel carrier 76 is revolutely mounted about the axle 75, and the torque link 72 constrains the rotation of the carrier 76. (The torque link 72 may be either above or below the trailing arm 71.) In this arrangement, the driving torque produced between the crown wheel carrier 76 and the rear wheel 74 cannot be transmitted to the sprung mass 83 by the trailing arm 71, because the trailing arm can only transmit forces along its longitudinal axis. The sprung mass 83, trailing arm 71, crown wheel carrier 76 and torque link 72 thus constitute a planar four-bar linkage system, which linkage defines the motion of the crown wheel carrier 76 as the suspension moves up and down. An imaginary point called a “Virtual pivot and Force center,” labeled VpFc, is the instant center of rotational motion of the wheel carrier 76, and is analogous to the ApFc of the simple trailing arm rear suspension system of FIG. 6. The Line of Action LoA for this type of rear suspension is shown in FIG. 10 as defined between the tire contact patch centroid TrCpt and the Virtual pivot and Force center VpFc. With this type of trailing arm rear suspension, there is greater design flexibility than for the simple trailing arm suspension of FIGS. 6 through 8, thereby allowing for a wider range of anti-squat, especially lower amounts of anti-squat.
FIG. 11 provides a top sectional view of a prior art shaft drive, trailing arm with torque link, motorcycle rear suspension, the view cut along a plane defined by the trailing arm pivot TAp and the wheel axis Wp. The driving torque DT is created by a driving pinion 77 working against the crown wheel 78, both of which are enclosed in the crown wheel carrier 76 on the axis 75 of the wheel 74. A braking torque may be created by the brake caliper 79 working against the brake disc 80. The torque on a drive shaft 82 is reacted by the trailing arm pivot axis TAp, and does not impart torque to swing the arm 71 about the pivot axis TAp. This type of rear suspension would require two universal joints 81, as well as a slip joint in the drive shaft (not shown), to provide the required degree of freedom of the crown wheel carrier 76. If provided, a hub motor would provide torque in a similar manner as the shaft drive, producing torque between a hub motor carrier (similar to the crown wheel carrier) and the wheel 74.
Anti-Squat in Arbitrary Trailing Arm with Torque Link Rear Suspensions
FIG. 12 shows a prior art (BMW® Paralever) arbitrary trailing arm with torque link rear suspension on a motorcycle 90. This arbitrary trailing arm system includes of a trailing arm 91, a torque link 92, an arbitrary pivot 93, a crown wheel carrier 96, a wheel axle 95 (about axis Wp), a rear wheel 94, a motorcycle sprung mass 103, a front suspension 64 and a front wheel 65. The trailing arm 91 is revolutely mounted to the sprung mass 103 by the trailing arm pivot TAp1. The arbitrary pivot 93 is fixed to the trailing arm 91 with its axis (TAp2) parallel to the axis of the trailing arm pivot TAp1. The crown wheel carrier 96 is revolutely mounted about the arbitrary pivot 93 axis TAp2, and the torque link 92 constrains the rotation of the carrier 96. The torque link 92 is allowed to rotate about pivot TLp2 connecting the torque link 92 and the crown wheel carrier 96, and about the pivot TLp1 between the torque link 92 and the motorcycle chassis 103. The wheel axle is revolutely mounted on pivot Wp to the crown wheel carrier 96 which is parallel to the arbitrary pivot 93 axis TAp2. In this arrangement, the driving torque produced between the crown wheel carrier 96 and the rear wheel 94 cannot be passed to the sprung mass 103 by the trailing arm 91, which can transmit forces along its longitudinal axis only. The sprung mass 103, trailing arm 91, crown wheel carrier 96 and torque link 92 make up a planar four-bar linkage system which defines the motion of the crown wheel carrier 96 as the suspension moves up and down. A point called a “Virtual pivot and Force center,” VpFc, is the instant center of rotation of the axle carrier 96, and is analogous to the ApFc of the simple trailing arm rear suspension of FIG. 6. The line of action for this type of rear suspension is between the tire contact patch centroid TrCpt and the Virtual pivot and Force center, VpFc. As with the trailing arm with torque link rear suspension of FIG. 10, this type of trailing arm suspension has greater design flexibility than the simple trailing arm suspension from FIGS. 6 through 8, allowing for a wider range of anti-squat, especially lower amounts of anti-squat.
FIG. 13 is a top sectional view of a prior art shaft drive arbitrary trailing arm with torque link motorcycle rear suspension (similar to that seen in FIG. 12) cut along imaginary planes defined by the trailing arm pivot TAp1, arbitrary pivot 93 axis TAp2, and the wheel axis Wp. (Typically, these three pivot axes are not disposed in a single imaginary plane.) There is a drive shaft 102 for transmitting rotary power. The driving torque DT is created by a driving pinion 97 working against a crown wheel 98, both of which are enclosed in the crown wheel carrier 96. A braking torque may be created by the brake caliper 99 working against the brake disc 100. The torque on the drive shaft 102 is reacted by the trailing arm pivot axis TAp1, and does not impart torque to the swing the arm 91 about the pivot axis TAp1. This type of rear suspension requires two universal joints 101 in the drive shaft 102 to provide the required degree of freedom of the crown wheel carrier 96. If provided, a hub motor would provide torque in a similar manner as the shaft drive, producing torque between a hub motor carrier (similar to the crown wheel carrier) and the wheel 94.
Anti-Squat in Chain Driven Trailing Arm Rear Suspensions
FIGS. 14 and 15 present prior art trailing arm rear suspensions with chain drive on a motorcycle 110, which feature a trailing arm 111, a drive chain 112, with an upper run 112u and a lower run 112l, a wheel axle 115, a rear wheel 114, a driven pinion (or sprocket) 116, a driving pinion 117, a motorcycle sprung mass 123, a front suspension 64 and a front wheel 65. The trailing arm 111 is revolutely mounted to the sprung mass 123 by the trailing arm pivot TAp. The rear wheel axle 115 is fixed to the trailing arm parallel to the trailing arm pivot TAp. The rear wheel 114 is revolutely mounted to the axle 115. The driven pinion 116 is torsionally mounted to the rear wheel 114 either rigidly or through a compliant coupling and is centered about the axle 115 and engages with the chain 112. The chain 112 is also engaged with a driving pinion 117, and through the upper run 112u and the lower run 112l, drives the driven pinion 116. The chain 112, or flexible endless drive, can only transmit power through tension, the upper run 112u drives the vehicle forward. During engine braking, the lower chain run 112l is under tension and slows the vehicle down.
The chain driven trailing arm suspension can be analyzed in much the same way as the trailing arm with torque link, except that the tensioned chain run replaces the torque link and instead of pivots at each end of the torque link, the chain mates with the pinions at tangent points between the chain and pinion. FIG. 14 represents the vehicle accelerating forward with the upper chain run under tension. The Virtual pivot and Force center VpFc of the rear wheel is determined at the point the trailing arm centerline crosses the upper run chain center line. The Line of Action is then drawn between the tire contact patch centroid TrCpt and the Virtual pivot VpFc. The amount of anti-squat can then be determined in the same way as presented in FIG. 9 by calculating the height that the Line of Action crosses the vertical line through the front axle relative to the CG height Hcg.
FIG. 15 represents the vehicle decelerating under engine braking with the lower chain run under tension. The Virtual pivot and Force center VpFc of the rear wheel is determined at the point the trailing arm centerline crosses the lower chain run center line. The Line of Action is then drawn between the tire contact patch centroid TrCpt and the Virtual pivot VpFc. The amount of anti-rise can then be determined in the same way as presented in FIG. 9 by calculating the height that the Line of Action crosses the vertical line through the front axle relative to the CG height Hcg.
FIG. 16 presents a top section view of a prior art chain driven trailing arm motorcycle rear suspension cut along planes defined by the trailing arm pivot TAp, the wheel axis, and the axis of the driving pinion. (Typically, these axes are not coplanar.) The driving torque DT is created by the upper chain run 112u pulling on the driven pinion 116. During engine braking, the lower chain run 112l pulls on the driven pinion 116. For durability reasons, an endless chain 112 with no master link is typically used on street motorcycles or a synchronous toothed belt which requires less maintenance and allows longer life than a chain. It can be seen from FIG. 16, that to replace the chain or belt requires that the trailing arm and associated hardware be removed from the vehicle, increasing the time and labor involved. This is the sixth problem with prior art leaning narrow vehicles—difficult access to vehicle driveline maintenance items such as a final chain drive element. A “chain” drive system in this disclosure refers to a class of endless flexible loop drives that include roller chain, silent chain and belt drives of both the friction variety and toothed (positive drive) variety.
FIG. 17 presents a prior art trailing arm rear suspension with chain drive on a motorcycle with a coaxial driving pinion of equal size to the driven pinion. For this special case of the chain drive trailing arm suspension, the trailing arm and chain runs are always parallel. This implies that the Virtual pivot and Force center is located at infinity. The Line of Action is therefore parallel to the trailing arm, and the anti-squat will vary as the suspension moves. With a horizontal trailing arm, the Line of Action will be along the ground with zero anti-squat. At full droop, the anti-squat will have the largest value while at full bump, the anti-squat may have a negative value resulting in pro-squat geometry.
Although not shown, a trailing arm rear suspension with chain drive on a motorcycle with a coaxial driving pinion of different size than a driven pinion could be easily imagined. For this type of a system the Virtual pivot and Force center would not be located at infinity, but at some finite distance along the trailing center line, which would be same location during acceleration or engine braking. The amount of anti-squat could then be determined based on FIG. 9.
As discussed in the foregoing description of the prior art, having reference to FIG. 2B though FIG. 17, there thus are six main problems with prior art narrow leaning vehicles, which are:                1) Unstable vehicle behavior during acceleration;        2) Difficult to package long trailing arms;        3) Undesirable poor vehicle roll dynamics during braking;        4) Reduced vehicle performance because low power and reduced braking ability are required to not induce vehicle stability or handling problems;        5) Increased vehicle operator training and high skill requirements because of poor vehicle dynamic behavior and handling qualities;        6) Difficult access to vehicle driveline maintenance items such as a final chain drive element.        
The disclosures of all the patents cited hereinabove are hereby incorporated herein by reference. What is needed in the art is an improved suspension and driveline configuration which reduces or eliminates these problems.
Narrow leaning multi-track vehicles have suspension and driveline issues which are considerably different than either leaning single track vehicles (motorcycles) or low lean angle multi-track vehicles (automobiles, trucks or similar). In the case of leaning single track vehicles (motorcycles) the drive, brake and coupling forces such as lift or squat act in, or at least very close to, the vehicle vertical plane, and therefore do not provide significant roll moments acting on the vehicle. For low lean angle multi-track vehicles, because of the small lean angles (on the order of approximately 5° to 10°) the roll moments induced by driveline-suspension coupling are small when compared to roll moments due to cornering (and other lateral accelerations) in relation to the roll stiffness of the suspension. It is only in the combination in a “narrow leaning multi-track vehicle” which (a) can experience large lean angles (greater than approximately 15°) and (b) has a separation of the wheels by a track width, that creates the issues and problems with driveline-suspension coupling that create a significant and unstabilizing roll moment acting on the vehicle. Because the issues and problems associated with these significant roll moments only affect narrow leaning, multi-track, vehicles, the solutions to these issues and problems are relevant primarily or only to narrow leaning multi-track vehicles.
Accordingly, several objects and advantage of the presently disclosed method and apparatus are:                1) Elimination of unstable vehicle behavior during acceleration;        2) Improved vehicle roll dynamics during braking;        3) Improved packaging of the suspension with shorter trailing arms;        4) Improved vehicle performance with the use of increased power and braking forces without inducing vehicle stability or handling problems;        5) Reduced vehicle operator training and skill requirements by ensuring excellent vehicle dynamic behavior and handling qualities;        6) Improved access to vehicle driveline maintenance items such as a final chain drive element.        
Still further objects and advantages will become apparent from a consideration of the ensuing description and drawings.